Fermín S. V. Bazán


Office

Department of Mathematics
Federal University of Santa Catarina
88040-900 Florianopolis, SC Brazil
Email: fermin@mtm.ufsc.br
URL: http://www.mtm.ufsc.br/~fermin
Phone: +51 48-331.9221 
Fax: +51 48-331.9221   

  Research Interests

  • Numerical linear algebra
  • Inverse problems
  • Modal analysis

 For Students (in Portuguese)

Research Group: Numerical Analysis and Scientific Computing (Portuguese)

Publications, Technical Reports, etc

  • Refereed Papers

    • F. S. Viloche Bazán and L. S. Borges, GKB-FP:an algorithm for large-scale discrete ill-posed problems. BIT, DOI 10.1007/s10543-010-0275-3, 2010 (pdf-file).

    • F. S. Viloche Bazán, Chebyshev pseudospectral method for wave equation with absorbing boundary conditions that does not use a first order hyperbolic system, Math. and Comput. in Simulation, Vol. 80, pp. 2124-2133, 2010 (pdf-file).

    • K. H. Leem, G. Pelekanos and F. S. Viloche Bazán, Fixed-point iterations in determining a Tikhonov regularization parameter in Kirsch's factorization method, Appl. Math. And Computation, Vol. 216, Issue 12, pp. 3747-3753, 2010. (pdf-file)

    • M. W. Zibetti, F. S. V. Bazán and J. Mayer, Estimation of the parameters in regularized simulateneous Super-resolution. To appear in Pattern Recongnition Letters, 2010.

    • F. S. Viloche Bazán, K. H. Leem and G. Pelekanos, An application of a fixed point iteration method to object reconstruction, PIERS Online, Vol. 6, No. 3, 227-231, DOI 10.2529/PIERS090906182755, 2010 (pdf-file).

    • F. S. V. Bazán and J. B. Francisco, An improved fixed-point algorithm for determining a Tikhonov regularization parameter. Inverse Problems, 2009.

    • J. C. Oliveira F. S. V. Bazán, Poisson approach for evaluating numerical methods for the two-dimensional wave equation constrained to absorbing boundary conditions. Appl. Math. and Comput., vol. 209, p. 273-284, 2009.

    • F. S. V. Bazán, Nonnormality estimation in projection-type system realization methods. Num. Lin. Alg. With Appl, vol. 15, p. 969-983, 2008. (pdf-file)

    • F. S. V. Bazán, Fixed-point iterations in determining Tikhonov regularization parameter. Inverse Problems, vol. 24, p.035001-035001, 2008. (pdf-file)

    •  F. S. V. Bazán, Chebyshev Pseudospectral Method for Computing  Numerical Solution of  Convection-diffusion equation. Appl.  Math and Comput., vol. 200, p.537-546, 2008.   (pdf-file)

    • M. V. W. Zibetti, F. S. V. Bazán and J. Mayer, Determining the regularization parameters for super-resolution problems. Signal Processing, vol. 88, no. 12, p. 28902901, 2008.

    • P. C. Calegari and F. S. V. Bazán, Spectral analysis of a Chebyshev pseudospectral method for wave propagation with transparent boundary conditions. TEMA, vol.8(2), p. 201-210, 2007.

    • F. S. V. Bazán and S. Gratton, An explicit Jordan Decomposition of Companion Matrices, TEMA, (pdf-file)

    • F. S. V. Bazán, Matrix polynomials with partially prescribed eigenstrucutre: Eigenvalue sensitivity and condition estimation. To appear in Comp. Appl. Math, 2005 (pdf-file)

    • F. S. V. Bazán and C. Cunha, Solving damped wave equations with the method of lines and quadratic matrix eigenvalues. Far East J. Appl. Math. 17(1) (2004), 105-120.

    • F. S. V. Bazán, Eigensystem realization algorithm: Reformulation and system pole perturbation analysis. J. Sound and Vibration 274 (2004), 433-444.

    • E. Kraemer and F. S. V. Bazán, Some measures of non normality of matrices (in Portuguese). Tema Vol. 4(1), pp. 61-70, 2003 .

    • F. S. V. Bazán, Error analysis of signal zeros: a projected companion matrix approach, Lin. Alg. Appl. Vol. 369 pp. 153-167, 2003 (pdf file)

    • F. S. V. Bazán, CGLS-GCV: a hybrid algorithm for solving low-rank-deficient problems. Appl. Num. Math. 47, pp. 91-108, 2003. (pdf-file)

    • F. S. V. Bazán,  Conditioning of rectangular Vandermonde matrices with nodes in the unit disk, SIAM J. Mat. Anal. Appl. Vol. 21(2) pp. 679-693, 2000.

    • F. S. V. Bazán and Ph. L. Toint, Error analysis of signal zeros from a related companion matrix eigenvalue problem, Appl. Math Letters, Vol. 14, pp. 859-866, 2001.

    • F. S. V. Bazán and Ph. L. Toint, Singular value analysis of predictor matrices, Mechanical Systems and Signal Processing, Vol. 15(4), pp. 667-683, 2001.

    • F. S. V. Bazán and Ph. L. Toint, Conditioning of infinite Hankel matrices of finite rank, Systems and Control Letters, Vol. 41, pp. 347-359, 2000.

    • F. S. V. Bazán, Sensitivity eigenanalysis of single shift-invariant subspace-based methods, Signal Processing, Vol. 80, pp. 89-100, 2000.

    • M. I. Cardoso and F. S. V. Bazán, Fast signal subspace computation in solving rank-deficient problems (in Portuguese), Tema, Vol.1, Part. 1, pp. 29-44, 2000.

    • F. S. V. Bazán, Sensitivity eigenvalue analysis in recovering exponential data (in Portuguese), Tema, Vol.1, Part. 2, pp. 289-302, 2000.

    • L. H. Bezerra and F. S. V. Bazán, Eigenvalue locations of Generalized Companion Predictor matrices, SIAM J. Matrix. Anal. Appl. Vol. 19(4) pp. 886-897, 1998.

    • F. S. V. Bazán and L. H. Bezerra, On zero locations of predictor polynomials, Num. Lin. Alg. Appl., Vol. 4(6), pp. 459-468, 1997.

    • F. S. V. Bazán and C. Bavastri, An optimized pseudo-inverse algorithm (OPIA) for multi-input multi-output modal parameter identification, Mechanical Systems and Signal Processing, Vol. 10, pp. 365-380, 1996.

    • C. Cunha and F. S. V. Bazán , An iterative method for the numerical inversion of Laplace Transforms, Math. Of Computations, Vol. 64(211), pp. 1193-1198, July 1995.

    • F. S. V. Bazán and P. G. Kurka, A Prony-moments method for parameter identification in overdetermined systems, Mechanical Systems and Signal Processing, Vol. 8(2), march, pp.145-154, 1994.

    • C. Cunha and F. S. V. Bazán , The Laguerre functions in the inversion of the Laplace Transform, Inverse Problems, Vol.9, pp. 57-68, 1993.

  • Technical Reports and Preprints.

    PostScript versions of some technical reports and preprints are available:

    • F. S. V. Bazán, An explicit Jordan Decomposition of Companion Matrices pdf-file

    • F. S. V. Bazán, Eigensystem realization algorithm: Reformulation and system pole perturbation analysis. Submitted to J. Sound and Vibration, Aug. 2002. (ps file)

    • F. S. V. Bazán, Ph. L. Toint and M. C. Zambaldi, A conjugate-Gradients based method for Harmonic Retrieval that does not use explicit signal subspace computation, Tech. rep. 16, Department of Mathematics, FUNDP, Namur Belgium, November 1997.

  • Talks

    • An Explicit Jordan Decomposition of Companion Matrices, XXVIII CNMAC- São Paulo, 2005. Slides (pdf-file)

    • Influência da Variação do Espectro em Computação Científica. Encontro Univ., UFSC, Nov. , 2005. Slides (pdf-file)

    • Solução Numérica da Equação da Onda Amortecida através do Método das Linhas e Auto-pares de Polinômios Matriciais Quadráticos. Seminário Brasileiro de Análise, UNIRIO, R.J., Nov. 2005. Slides (pdf-file)

  • Books and Lecture Notes

    • Eigenvalues of Matrix Polynomials, Sensitivity, Computation and Applications (in Portuguese). Edited by IMPA, Rio de Janeiro - Brazil, July 2003. ISBN: 85-244-0206-7, 167 pag. Short course prepared for the XXIV Coloquio de Matemática, IMPA July 2003. (pdf-file)Slides: Part I (slide1), Parts II-III (slide2-3), Part IV, (slide4) Part V (slide5)

    • Álgebra Linear Computacional e Problemas de posto incompleto. Monografia de Minicurso presentado no XXIII CNMAC, Setembro 2000, Santos SP, Brasil (com M. I. Cardoso). Editado pela SBMAC, Santos 2000. 86 pag.

    • Métodos de decomposição parcial do espectro de uma matriz. Monografia de Minicurso presentado no XXIV CNMAC, Setembro 2001, Belo Horizonte MG, Brasil (com L. H. Bezerra). Editado pela SBMAC, Belo Horizonte 2001, 43 pag.